A multi-factor integrated satellite optimal collision avoidance control method and system

Abstract

The application discloses a satellite optimal collision avoidance control method and system integrating multiple factors and belongs to the technical field of spacecraft orbit control. The application establishes an orbit differential equation of both collision targets based on a Gauss perturbation equation; establishes a continuous variable direction thrust direction angle function based on Fourier series fitting; establishes an optimal control model of collision avoidance-return orbit integrating multiple factors; sets an optimization target based on weight distribution, solves the continuous thrust direction angle and switching time through an optimization algorithm, and realizes mission satellite avoidance control. The application can solve the problem that the existing technology only considers safety factors for collision avoidance of non-cooperative targets, which leads to difficult subsequent consecutive space operation and reduced satellite mission efficiency, and the orbit control scheme is simple and reliable, meets the actual engineering needs, and effectively reduces the satellite orbit deviation risk caused by satellite collision avoidance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of spacecraft orbit control technology, and relates to a satellite optimal collision avoidance control method and system considering multiple factors. BACKGROUND

[0002] With the rapid pace of human space exploration, the space environment outside the earth has changed greatly, and a large number of space debris are scattered in the near-earth space and run at high speed on their orbits around the earth. The satellite collision avoidance escape problem based on orbit control technology is paid more and more attention. In the face of the approaching threat from non-cooperative targets, the orbit control technology for collision avoidance through rapid maneuvering escape is applied to in-orbit service, space attack and defense and other space fields. The collision avoidance orbit control problem mainly studies the orbit motion between two close space vehicles, establishes the state differential equation of the two, and gives a guidance control method.

[0003] Compared with the uncertainty of the orbit of the non-cooperative target, most of the application satellites run on near-circular orbits. Considering various error disturbances in practice and the rapidity of the collision avoidance event, the orbit can be approximated as a circular orbit, and the average orbit element is used for description, and the thrust is applied to change the orbit parameters to achieve the required control. The existing method usually uses the collision threat observation information generated by the ground observation station or the on-board autonomous observation load to determine the optimal avoidance maneuver direction based on various collision risk representation quantities; or describes the maneuver control problem of the task satellite as a nonlinear programming problem to optimize the collision avoidance orbit and ensure the safe operation of the task satellite. Among them, the orbit control in actual engineering depends on the maneuvering ability of the satellite itself and the fuel consumption limit, etc., which is a test for the performance, power consumption and reliability of the task satellite. In addition, in the face of the approaching threat of non-cooperative targets, the optimal avoidance scheme considering only the safety factor may cause the satellite to deviate from the original orbit after control, which is not conducive to subsequent coherent space operation and completion of satellite tasks. For the comprehensive multi-factor anti-collision problem in the process of rapid approaching of non-cooperative targets, there is no effective solution at present. SUMMARY

[0004] The technical problem solved by the present application is that the prior art only considers the safety factor of the task satellite for collision avoidance of non-cooperative targets.

[0005] In view of the above problems, the present application provides a collision avoidance-return orbit optimal control solving method which fully considers the fuel factor, safety factor, task factor and configuration factor of the task satellite. The method is simple and reliable, meets the actual engineering needs, and can meet the flexibility and rapidity requirements of the task under the condition of close collision avoidance.

[0006] The technical scheme adopted by the present application is: a satellite optimal collision avoidance control method considering multiple factors, comprising:

[0007] establishing the orbit differential equation of the collision threat target based on the Gauss perturbation equation;

[0008] establishing a direction angle function of the continuous variable thrust based on Fourier series fitting;

[0009] establishing a comprehensive multi-factor collision avoidance-return orbit optimal control model by combining the orbit differential equation and the direction angle function of the continuous variable thrust;

[0010] setting an optimization target based on weight distribution, solving the optimal solution of the collision avoidance-return orbit optimal control model through an optimization algorithm, obtaining the direction angle of the continuous thrust and the switching time, and controlling the mission star to avoid the collision threat target based on the direction angle of the continuous thrust and the switching time.

[0011] As an aspect of the present application, the method for establishing the orbit differential equation of the mission star and the collision threat target based on the Gauss perturbation equation is:

[0012] The on-orbit state of the spacecraft is described by using the orbit elements at each time, the orbit element differential equation of the collision parties under the continuous thrust is constructed by using the Gauss perturbation equation, the decomposition of the thrust in the tangential direction, the normal direction and the sub-normal direction of the velocity of the mission star is denoted as (f t ,f m ,f h ), and the orbit differential equation of the mission star based on the Gauss perturbation equation is established.

[0013]

[0014] wherein the orbit elements of the mission star are , a is the semi-major axis of the mission star, e is the eccentricity of the mission star, i is the orbit inclination of the mission star, Omega is the ascending node right ascension of the mission star, omega is the perigee amplitude angle of the mission star, u is the latitude amplitude angle of the mission star, v is the orbit velocity of the mission star, p is the orbit semi-latus rectum, theta is the true anomaly of the mission star, r is the geocentric distance of the mission star, f t is the tangential component of the thrust per unit mass of the mission star in the forward direction of the velocity vector of the mission star, f m is the normal component of the thrust per unit mass of the mission star in the direction away from the curvature center in the orbit plane of the mission star, f h is the sub-normal component of the thrust per unit mass of the mission star in the direction of the momentum vector H of the mission star, e m is the unit vector in the tangential direction of the velocity of the mission star, e t is the unit vector in the normal direction of the velocity of the mission star, e h is the unit vector in the sub-normal direction of the velocity of the mission star, and mu is the gravitational constant of the earth.

[0015] The orbit differential equation of the collision threat target is established based on the Gauss perturbation equation:

[0016]

[0017] Wherein, the orbit root of the collision threat target is is the derivative of the physical quantity with respect to time, a target is the semi-major axis of the collision target, e target is the eccentricity of the collision target, i target is the orbit inclination of the collision target, Ω target is the ascending node right ascension of the collision target, ω target is the perigee amplitude of the collision target, u target is the latitude amplitude of the collision target star, v target is the orbit velocity of the collision target; p target is the orbit semi-diameter, θ target is the true anomaly of the collision target, r target is the geocentric distance of the collision target; f ttarget is the tangential component of the perturbation force on the unit mass of the collision target along the forward direction of the velocity vector of the collision target, f mtarget is the normal component of the perturbation force on the unit mass of the collision target along the direction away from the curvature center in the orbit plane of the collision target, f htarget is the vice-normal component of the perturbation force on the unit mass of the collision target along the direction of the momentum moment vector H target of the collision target, e mtarget is the unit vector of the tangential velocity of the collision target, e ttarget is the unit vector of the normal velocity of the collision target, e htarget is the unit vector of the vice-normal velocity of the collision target, μ is the earth gravity constant;

[0018] In the case that the thrust of the task star at each time is known, the orbit differential equation of the task star is integrated to obtain the orbit of the task star under the control of the thrust, and the orbit differential equation of the collision threat target is integrated to obtain the orbit of the collision threat target without control. Thus, the construction of the orbit differential equation of the collision target based on the Gauss perturbation equation is completed.

[0019] As an aspect of the present application, the method for establishing the direction angle function of the continuous variable direction thrust based on the Fourier series fitting is:

[0020] The expression formula of the continuous variable direction control thrust of the task star is:

[0021] F x = F cos β cos α

[0022] F y = F cos β sin α,

[0023] F z = F sin β

[0024] Wherein, the component of the thrust F of the mission star in the direction of (e m ,e t ,e h ) is (F x ,F y ,F z );The thrust direction angle of the mission star is (α,β), α is the angle between the projection of the mission star thrust vector in the (e m ,e t ) plane and e m , with the e h axis right-hand rule direction being positive, β is the angle between the mission star thrust vector F and its projection in the (e m ,e t ) plane, with the e h axis positive direction being positive;e m is the unit vector of the mission star velocity tangential direction, e t is the unit vector of the mission star velocity normal direction, e h is the unit vector of the mission star velocity subnormal direction, (e m ,e t ) is the platform in which the mission star velocity tangential direction and the mission star velocity normal direction are located;

[0025] In the expression formula of the mission star sustained variable direction control thrust, the change of the thrust direction angle (α,β) with time is described by Fourier series fitting, and the sustained variable direction thrust direction angle function based on Fourier series fitting is:

[0026]

[0027] Wherein, the first item parameter, the second item parameter, the third item parameter, the fourth item parameter and the first item parameter of the Fourier series fitting of the thrust direction angle α are [a0,a1,a2,a3,a4], and the first item parameter, the second item parameter, the third item parameter, the fourth item parameter and the first item parameter of the Fourier series fitting of the thrust direction angle β are [b0,b1,b2,b3,b4].

[0028] As an aspect of the application, the method for establishing a comprehensive multi-factor collision avoidance-return orbit optimal control model is combined with the orbit differential equation and the sustained variable direction thrust direction angle function:

[0029] S031, determining the optimization variable of the collision avoidance-return orbit optimal control model as: x=[a0,a1,a2,a3,a4,b0,b1,b2,b3,b4,t1,t2,t3] Twherein [a0, a1, a2, a3, a4, b0, b1, b2, b3, b4] are the first term parameters, the second term parameters, the third term parameters, the fourth term parameters and the first term parameters of the Fourier series fitting of the thrust direction angle a and the first term parameters, the second term parameters, the third term parameters, the fourth term parameters and the first term parameters of the Fourier series fitting of the thrust direction angle b; the moment when the collision threat target approaches to the boundary of the anti-collision sensing range of the mission star is recorded as t = t0, the switch-on and switch-off moments of the two continuous thrust maneuvers are [t0, t1, t2, t3], wherein t0 is the first switch-on moment of the thruster, t1 is the first switch-off moment of the thruster, t2 is the second switch-on moment of the thruster, and t3 is the second switch-off moment of the thruster; the maneuver starts immediately when the collision threat target enters the boundary of the anti-collision sensing range of the mission star, so t0 = 0 s is set;

[0030] S032, the optimization constraints of the collision avoidance-return orbit optimal control model are determined as wherein Ax≤b is a linear constraint inequality, and the constraint parameters are:

[0031]

[0032] wherein A is the linear constraint matrix of the mission star optimal control model, x is the optimization variable of the mission star orbit optimal control model, and b is the linear constraint vector of the mission star orbit optimal control model;

[0033] lb<x<ub is a control quantity upper and lower bound constraint inequality, and the constraint parameters are:

[0034]

[0035] wherein lb is the lower bound of the optimization variable of the mission star orbit optimal control model, ub is the upper bound of the optimization variable of the mission star orbit optimal control model, t max is the maximum allowed completion time of single avoidance control;

[0036] c(x)≤0 is a nonlinear constraint function, expressed as:

[0037]

[0038] wherein (Δa final (x), Δe final (x), Δi final (x), ΔΩ final (x), Δω final (x), Δu final (x)) is the orbit element offset at the control end moment, Δa final (x) is the semi-major axis offset of the mission star at the control end moment, Δe final(x) is the eccentricity offset of the mission star at the control end time, Δi final (x) is the orbit inclination offset of the mission star at the control end time, ΔΩ final (x) is the ascending node right ascension offset of the mission star at the control end time, Δω final (x) is the perigee argument offset of the mission star at the control end time, Δu final (x) is the latitude argument offset of the mission star at the control end time, (Δa fmax , Δe fmax , Δi fmax , ΔΩ fmax , Δω fmax , Δu fmax ) is the maximum orbit root offset allowed by the mission star, Δa fmax is the maximum semi-major axis offset allowed by the mission star, Δe fmax is the maximum eccentricity offset allowed by the mission star, Δi fmax is the maximum orbit inclination offset allowed by the mission star, ΔΩ fmax is the maximum ascending node right ascension offset allowed by the mission star, Δω fmax is the maximum perigee argument offset allowed by the mission star, Δu fmax is the maximum latitude argument offset allowed by the mission star, l min (x) is the closest distance between the mission star and the collision target during the avoidance maneuver, l safe is the minimum safety distance of the mission star collision avoidance;

[0039] S033, combined with the orbit differential equation and the direction angle function of the continuous variable thrust, establishes the objective function of the collision avoidance-return orbit optimal control model, which is:

[0040] J=k1J1+k2J2+k3J3,

[0041] Where [J1, J2, J3] are the optimization objectives reflecting the mission factors, the optimization objectives reflecting the configuration factors and the optimization objectives reflecting the fuel factors, respectively, [k1, k2, k3] are the first target weight, the second target weight and the third target weight, and the sum of the first target weight, the second target weight and the third target weight is 1.

[0042] As an aspect of the present application, in the objective function of the collision avoidance-return orbit optimal control model:

[0043] Where N cover (x) is the number of target coverage completed by the mission star, N target is the total number of coverage targets;

[0044] (Δu tmax (x),Δi tmax (x),ΔΩ tmax (x)) is the maximum value of the orbit root number offset of the whole course of the mission star maneuver, Δu tmax (x) is the maximum value of the latitude amplitude angle offset of the whole course of the mission star maneuver, Δi tmax (x) is the maximum value of the orbit inclination offset of the whole course of the mission star maneuver, ΔΩ tmax (x) is the maximum value of the ascending node right ascension offset of the whole course of the mission star maneuver, (Δu max ,Δi max ,ΔΩ max ) is the maximum orbit root number offset allowed by the mission star, Δu max is the maximum latitude amplitude angle offset allowed by the mission star, Δi max is the maximum orbit inclination offset allowed by the mission star, ΔΩ max is the maximum ascending node right ascension offset allowed by the mission star;

[0045] t max is the maximum fuel consumption corresponding to the start-up time allowed by the single avoidance of the mission star, t1 is the first time when the thruster is shut down, t2 is the second time when the thruster is started, and t3 is the second time when the thruster is shut down.

[0046] As an aspect of the present application, the optimal solution of the collision avoidance-return orbit optimal control model is solved by an optimization algorithm based on the weight distribution setting optimization target, and the continuous thrust direction angle and the start-stop time are obtained, and the method for controlling the mission star to avoid the collision threat target based on the continuous thrust direction angle and the start-stop time is:

[0047] The optimization target parameters [k1, k2, k3, J1, J2, J3] of the mission star avoidance-return orbit optimal control model are set, and the constraint parameters [t max ,Δa fmax ,Δe fmax ,Δi fmax ,ΔΩ fmax ,Δω fmax ,Δu fmax ,l safe ] are set, wherein [J1, J2, J3] are the optimization targets reflecting the mission factors, the optimization targets reflecting the configuration factors, and the optimization targets reflecting the fuel factors, [k1, k2, k3] are the first target weight, the second target weight, and the third target weight, t max is the maximum completion time allowed by the single avoidance control, Δa fmax is the maximum final semi-major axis offset allowed by the mission star, Δe fmax is the maximum final eccentricity offset allowed by the mission star, Δifmax the maximum offset of the final orbit inclination allowed for the mission satellite, ΔΩ fmax the maximum offset of the final ascending node right ascension allowed for the mission satellite, Δω fmax the maximum offset of the final argument of perigee allowed for the mission satellite, Δu fmax the maximum offset of the final latitude argument allowed for the mission satellite, l safe the minimum safety distance for collision avoidance of the mission satellite;

[0048] On this basis, an initial value is given to the optimization variable x of the optimal control model of the mission satellite orbit, and an optimization algorithm is used to solve the collision avoidance-return orbit of the mission satellite with two-section continuous variable thrust maneuvers, so that the objective function of the collision avoidance-return orbit optimal control model is optimal under the condition of meeting the constraint condition, and the optimal control strategy result, i.e., the thrust direction angle and the switching-on time of the mission satellite, is obtained, so as to realize the optimal avoidance control of the mission satellite.

[0049] As an aspect of the present application, the optimization algorithm is a nonlinear programming solver, a genetic algorithm or a particle swarm algorithm.

[0050] The present application also provides a satellite optimal collision avoidance control system integrating multiple factors, which is used for executing the satellite optimal collision avoidance control method integrating multiple factors.

[0051] The first module is used for establishing the orbit differential equation of the collision target based on the Gauss perturbation equation, and describing the real-time motion state of the collision target.

[0052] The second module is used for establishing the continuous variable thrust direction angle function based on the Fourier series fitting.

[0053] The third module is used for establishing the optimal control model of the collision avoidance-return orbit integrating multiple factors.

[0054] The fourth module is used for solving the continuous thrust direction angle and the switching-on time, and realizing the optimal control of the mission satellite.

[0055] Compared with the prior art, the present application has the following advantages:

[0056] (1) The present application faces the collision avoidance demand of non-cooperative targets, and proposes an optimal control method of variable continuous thrust based on the Fourier series parameters and the switching-on time, which is simple and reliable, and easy to realize high-precision control.

[0057] (2) The application fully considers the actual task satellite maneuvering ability and task requirement restrictions in the case of ensuring collision avoidance safety distance, and designs a two-stage maneuvering orbit control scheme considering fuel, configuration, task and safety factors in detail, and the control method can realize close-range avoidance orbit control in the case of approaching collision threat;

[0058] (3) The application considers the anti-collision requirement of the task satellite in the approaching process, and performs safety distance constraint at each time of the full maneuvering process, effectively avoiding the risk that the intersection point changes due to orbit control and the new collision point is difficult to predict. DETAILED DESCRIPTION

[0059] The application will be further described in detail below with reference to specific embodiments.

[0060] The embodiment fully considers fuel factors, safety factors, task factors and configuration factors of the task satellite, and designs an optimal control solving method for satellite collision avoidance-return orbit, effectively reduces the satellite orbit deviation and task failure risk caused by satellite collision avoidance, and provides certain reference and reference for collision threat avoidance control of space non-cooperative targets.

[0061] Embodiment 1

[0062] The embodiment discloses a satellite optimal collision avoidance control method considering multiple factors, comprising:

[0063] Step 1, establishing an orbit differential equation of the task satellite based on the Gauss perturbation equation and an orbit differential equation of the collision threat target based on the Gauss perturbation equation;

[0064] It can be understood that in the embodiment, the method for establishing the orbit differential equation of the task satellite and the collision threat target based on the Gauss perturbation equation is:

[0065] The on-orbit state of the spacecraft is described by using the orbit elements at each time, the orbit element differential equation of the collision parties under continuous thrust is constructed by using the Gauss perturbation equation, the decomposition of the thrust in the tangential, normal and binormal directions of the task satellite speed is denoted as (f t ,f m ,f h ), and the orbit differential equation of the task satellite based on the Gauss perturbation equation is:

[0066]

[0067] Wherein, the orbit elements of the task satellite are Let be the derivative of the physical quantity with time, a be the semi-major axis of the mission satellite, e be the eccentricity of the mission satellite, i be the orbital inclination of the mission satellite, Ω be the right ascension of the ascending node of the mission satellite, ω be the argument of perigee of the mission satellite, u be the argument of latitude of the mission satellite, v be the orbital velocity of the mission satellite; p be the semi-major orbital radius, θ be the true perigee of the mission satellite, and r be the distance from the Earth's center to the mission satellite; f t f is the tangential component of the thrust per unit mass of the mission satellite along the forward velocity vector of the mission satellite. m f is the normal component of the thrust per unit mass of the mission satellite along the orbital plane away from the center of curvature. h e is the secondary normal component of the thrust per unit mass of the mission satellite along the direction of the mission satellite's angular momentum vector H. m e is the unit vector along the tangent of the mission star's velocity. t e is the unit vector of the mission star's velocity normal. h is the unit vector of the mission star's velocity subnormal direction, and μ is the Earth's gravitational constant;

[0068] The orbital differential equation for a collision threat target based on the Gaussian perturbation equation is as follows:

[0069]

[0070] Among them, the orbital elements of the collision threat target are Let a be the derivative of a physical quantity with time. target e is the semi-major axis of the collision target. target Let i be the eccentricity of the collision target. target Ω represents the orbital inclination of the target object. target Let ω be the right ascension of the ascending node of the colliding target. target u is the perigee argument of the target being collided with. target v is the latitudinal argument of the target star. target p represents the trajectory velocity of the collision target. target Let θ be the semi-major diameter of the track. target r is the true perimeter angle of the collision target. target f is the distance from the center of the target to the ground. ttarget f is the tangential component of the perturbation force per unit mass of the colliding target along the forward velocity vector of the colliding target. mtarget f is the normal component of the perturbation force per unit mass of the colliding target along the plane of the colliding target's trajectory, away from the center of curvature. htarget The perturbation force per unit mass of the colliding target along the angular momentum vector H of the colliding target. target The binormal component of the direction, e mtarget e is the unit vector of the tangential velocity of the colliding target. ttarget e is the unit vector normal to the velocity of the colliding target. htargetis the unit vector of the velocity of the target, μ is the gravitational constant of the earth;

[0071] In the case of known thrust of the mission star at each time, the orbit differential equation of the mission star is integrated to obtain the orbit of the mission star under the control of the thrust, and the orbit differential equation of the collision threat target is integrated to obtain the orbit of the collision threat target without control; thus, the construction of the orbit differential equation of both sides of the collision target based on the Gauss perturbation equation is completed;

[0072] Step two, the method for establishing the direction angle function of the continuously variable thrust based on Fourier series fitting is as follows:

[0073] It can be understood that, in the embodiment, the method for establishing the direction angle function of the continuously variable thrust based on Fourier series fitting is as follows:

[0074] Since the optimal avoidance maneuver needs a series of continuously acting forces to change direction constantly, the variable direction continuous thrust orbit transfer model is set to be used for mission star avoidance control, and the specific maneuver mode is that the thrust size of the satellite thruster is constant, the thrust direction is continuously derivable, the Fourier series even extension approximation is selected to represent the change function of the direction angle of the thrust with time, according to the theory of Fourier series, any periodic function can be written as an infinite series composed of sine and cosine functions:

[0075]

[0076] The change of the function with time t is extended to obtain the periodic function, and experience shows that generally the first five terms of the series can obtain a good approximation effect;

[0077] The expression formula of the continuously variable control thrust of the mission star is:

[0078] F x = F cosβcosα

[0079] F y = F cosβsinα,

[0080] F z = F sinβ

[0081] Wherein, the components of the thrust F of the mission star in the (e m ,e t ,e h ) direction are (F x , F y , F z ); the direction angle of the thrust of the mission star is (α, β), α is the angle between the projection of the thrust vector of the mission star in the (e m ,e t ) plane and e m , and β is the angle between the thrust vector of the mission star and eh The right-hand rule direction is positive, and β is the angle between the task star thrust vector F and its projection in the (e m t ) plane, e h The positive direction is positive; e m is the unit vector of the tangential velocity of the task star, e t is the unit vector of the normal velocity of the task star, e h is the unit vector of the subnormal velocity of the task star, and (e m t ) is the platform in which the tangential velocity of the task star and the normal velocity of the task star are located.

[0082] In the expression formula of the task star continuous variable direction control thrust, the thrust direction angle (α, β) changes with time and is described by Fourier series fitting. The continuous variable direction thrust direction angle function based on Fourier series fitting is:

[0083]

[0084] Where the first five parameters of the Fourier series fitting of the thrust direction angle α are [a0, a1, a2, a3, a4], and the first five parameters of the Fourier series fitting of the thrust direction angle β are [b0, b1, b2, b3, b4]. In this way, the change of the thrust direction angle (α, β) with time t can be represented by ten coefficients. The thrust direction angle function coefficients are given, and the task star control orbit can be solved by combining the orbit differential equation, which is convenient for orbit design optimization.

[0085] Step three, establish a comprehensive multi-factor collision avoidance-return orbit optimal control model combining the orbit differential equation and the continuous variable direction thrust direction angle function.

[0086] It can be understood that in the embodiment, the method for establishing a comprehensive multi-factor collision avoidance-return orbit optimal control model combining the orbit differential equation and the continuous variable direction thrust direction angle function is:

[0087] The general formulation of the continuous thrust orbit optimization design problem is as follows: under a given dynamic model and certain task constraints, design an orbit path controlled by continuous thrust, so that the spacecraft can move from the initial state to the target state within the specified constraints, and in this process, the objective function is optimal (such as fuel or configuration or work efficiency index, etc.); the following establishes a task star orbit maneuver model based on the continuous thrust direction angle function in step two, and gives the mathematical description of the nonlinear programming form of the problem;

[0088] ​​The whole maneuvering process of the mission satellite collision avoidance is divided into three stages, i.e. the starting segment, the sliding segment and the ending segment; the termination time of the three segments is respectively t1, t2 and t3, the thruster is applied in the time period of 0-t1 (i.e. the starting segment) and t2-t3 (i.e. the ending segment), and is closed in the time period of t1-t2 (i.e. the sliding segment); the mission satellite is separated from the original orbit in the starting segment, completes the rendezvous with the collision threat in the sliding segment, and returns to the original orbit in the ending segment, and the specific steps of establishing the optimization model are as follows:

[0089] S031, determining the optimization variable of the collision avoidance-return orbit optimal control model as x = [a0, a1, a2, a3, a4, b0, b1, b2, b3, b4, t1, t2, t3] T Wherein, [a0, a1, a2, a3, a4, b0, b1, b2, b3, b4] are the first item parameters, the second item parameters, the third item parameters, the fourth item parameters and the first item parameters of the Fourier series fitting of the thrust direction angle α and the first item parameters, the second item parameters, the third item parameters and the fourth item parameters of the Fourier series fitting of the thrust direction angle β; the time when the collision threat target approaches to the boundary of the mission satellite anti-collision sensing range is recorded as t = t0, the switching-on and switching-off time of the two continuous thrust maneuvers is [t0, t1, t2, t3], wherein t0 is the first switching-on time of the thruster, t1 is the first switching-off time of the thruster, t2 is the second switching-on time of the thruster, and t3 is the second switching-off time of the thruster; the maneuvering is started immediately when the collision threat target enters the boundary of the mission satellite anti-collision sensing range, and t0 = 0 s is set;

[0090] The reason is that the optimization variable x is determined; if the mass m of the mission satellite, the thrust size F of the thruster and the initial state λ1 of the spacecraft are given, the terminal state λ2 of the return orbit can be obtained by integrating the orbit differential equation under the condition that the mission satellite has no maneuvering (i.e. F = 0); under the above conditions, the problem has 14-dimensional variables, of which 10-dimensional variables are the function coefficients of the thrust direction angle, in addition, two maneuvers are set in the process of one-time avoidance-return, i.e. four switching-on and switching-off times t0, t1, t2, t3; for the near-earth object collision warning problem, it is known from experience that the earlier the switching-on starting time of the avoidance, the more favorable it is for the avoidance, therefore, the maneuvering is started immediately when the collision threat target enters the boundary of the mission satellite anti-collision sensing range, and t0 = 0 s, and the optimization variable can be written as a 13-dimensional vector;

[0091] S032, determining the optimization constraint function considering the configuration factor and the safety factor, the constraint function of the problem can be divided into the following three types: linear constraint, nonlinear constraint and upper and lower bound constraint, i.e. the optimization constraint of the collision avoidance-return orbit optimal control model is Wherein, Ax≤b is a linear constraint inequality, the expression meaning is t1 < t2 < t3, and the constraint parameters are:

[0092]

[0093] where A is the linear constraint matrix of the optimal control model of the mission satellite, x is the optimization variable of the optimal control model of the orbit of the mission satellite, and b is the linear constraint vector of the optimal control model of the orbit of the mission satellite;

[0094] lb < x < ub is a control variable upper and lower bound constraint inequality, and the constraint parameter is:

[0095]

[0096] where lb is the lower bound of the optimization variable of the optimal control model of the orbit of the mission satellite, ub is the upper bound of the optimization variable of the optimal control model of the orbit of the mission satellite, t max is the maximum completion time allowed for single avoidance control;

[0097] c(x) ≤ 0 is a nonlinear constraint function, including two parts of orbit root constraint and collision avoidance constraint, and the specific function is to limit the orbit offset at the end of the maneuver and complete the collision avoidance at a safe distance, and is expressed as:

[0098]

[0099] where (Δa final (x), Δe final (x), Δi final (x), ΔΩ final (x), Δω final (x), Δu final (x)) is the orbit root offset at the end of the control, Δa final (x) is the semi-major axis offset of the mission satellite at the end of the control, Δe final (x) is the eccentricity offset of the mission satellite at the end of the control, Δi final (x) is the orbit inclination offset of the mission satellite at the end of the control, ΔΩ final (x) is the right ascension offset of the ascending node of the mission satellite at the end of the control, Δω final (x) is the argument of perigee offset of the mission satellite at the end of the control, Δu final (x) is the argument of latitude offset of the mission satellite at the end of the control, (Δa fmax , Δe fmax , Δi fmax , ΔΩ fmax , Δω fmax , Δu fmax ) is the maximum final orbit root offset allowed for the mission satellite, Δa fmax is the maximum final semi-major axis offset allowed for the mission satellite, Δe fmaxThe maximum eccentricity offset allowed for the mission satellite, Δi fmax The maximum inclination offset allowed for the mission satellite, ΔΩ fmax The maximum longitude of ascending node offset allowed for the mission satellite, Δω fmax The maximum argument of perigee offset allowed for the mission satellite, Δu fmax The maximum latitude offset allowed for the mission satellite, l min (x) is the minimum safety distance for the mission satellite to avoid collision safe The minimum safety distance for the mission satellite to avoid collision

[0100] S033, determining an optimization target considering the mission factor, the configuration factor and the fuel factor; under the condition that the optimization targets representing the factors are normalized, the multi-targets can be converted into a single target by using a weight distribution method, and a target function of the collision avoidance-return trajectory optimal control model is established by combining the orbit differential equation and the sustained variable direction thrust direction angle function, which is:

[0101] J=k1J1+k2J2+k3J3,

[0102] Wherein, [J1, J2, J3] are the optimization target reflecting the mission factor, the optimization target reflecting the configuration factor and the optimization target reflecting the fuel factor, respectively, [k1, k2, k3] are the first target weight, the second target weight and the third target weight, and the sum of the first target weight, the second target weight and the third target weight is 1.

[0103] It can be understood that in the target function of the collision avoidance-return trajectory optimal control model:

[0104] For the mission factor, taking the ground target coverage task as an example, the target coverage rate is selected as the optimization target J1, and then:

[0105]

[0106] Wherein, N cover (x) is the number of target coverage completed by the mission satellite, N target is the total number of target coverage;

[0107] For the configuration factor, the maximum configuration offset in the whole process of the maneuver is selected as the optimization target J2, and according to the configuration maintenance experience, in order to reduce the long-term influence of the initial deviation on the later configuration evolution, the main controlled orbit roots are (u, i, Ω), and then: (Δu tmax (x), Δi tmax (x), ΔΩ tmax (x)) is the maximum value of the orbit root offset of the mission satellite in the whole process of the maneuver, Δu tmax(x) is the maximum value of the latitude amplitude argument offset of the task star maneuvering whole process, Δi tmax (x) is the maximum value of the orbit inclination offset of the task star maneuvering whole process, ΔΩ tmax (x) is the maximum value of the ascending node right ascension offset of the task star maneuvering whole process, (Δu max , Δi max , ΔΩ max ) is the maximum orbit root offset allowed by the task star, Δu max is the maximum latitude amplitude offset allowed by the task star, Δi max is the maximum orbit inclination offset allowed by the task star, ΔΩ max is the maximum ascending node right ascension offset allowed by the task star;

[0108] For the fuel factor, since the continuous propulsion on time is proportional to the fuel consumption, the total on time of the task star twice maneuvering is taken as the optimization target J3, and then t max is the maximum fuel consumption corresponding to the on time of the task star single avoidance, t1 is the first time when the thruster is turned off, t2 is the second time when the thruster is turned on, and t3 is the second time when the thruster is turned off;

[0109] Step four, based on the weight allocation, the optimization target is set, the optimal solution of the collision avoidance-return orbit optimal control model is solved by an optimization algorithm, the continuous thrust direction angle and the on-off time are obtained, and the task star is controlled to avoid the collision threat target based on the continuous thrust direction angle and the on-off time;

[0110] It can be understood that in the embodiment, based on the weight allocation, the optimization target is set, the optimal solution of the collision avoidance-return orbit optimal control model is solved by an optimization algorithm, the continuous thrust direction angle and the on-off time are obtained, and the task star is controlled to avoid the collision threat target based on the continuous thrust direction angle and the on-off time, and the method is:

[0111] The optimization target parameters [k1, k2, k3, J1, J2, J3] and the constraint parameters [t max , Δa fmax , Δe fmax , Δi fmax , ΔΩ fmax , Δω fmax , Δu fmax , l safe ] of the task star avoidance-return orbit optimal control model are set, wherein [J1, J2, J3] are the optimization targets reflecting the task factor, the optimization target reflecting the configuration factor and the optimization target reflecting the fuel factor, [k1, k2, k3] are the first target weight, the second target weight and the third target weight, t max is the maximum completion time allowed by single avoidance control, Δafmax Δe is the maximum eccentricity offset allowed for the final orbit of the mission satellite fmax Δi is the maximum inclination offset allowed for the final orbit of the mission satellite fmax ΔΩ is the maximum orbit inclination offset allowed for the final orbit of the mission satellite fmax Δω is the maximum ascending node offset allowed for the final orbit of the mission satellite fmax Δu is the maximum argument of perigee offset allowed for the final orbit of the mission satellite fmax l is the maximum latitude offset allowed for the final orbit of the mission satellite safe is the minimum safety distance for collision avoidance of the mission satellite;

[0112] On this basis, a preliminary value of the optimization variable x of the optimal control model of the mission satellite orbit is given, and the optimization algorithm is used to solve the collision avoidance-return orbit of the mission satellite with two-stage continuous variable thrust maneuver, so that the objective function of the collision avoidance-return orbit optimal control model is optimal under the condition of meeting the constraint condition, and the optimal control strategy result, i.e. the thrust direction angle and the switching-on time of the mission satellite, is obtained, so as to realize the optimal avoidance control of the mission satellite;

[0113] Optionally, the optimization algorithm is a nonlinear programming solver, a genetic algorithm or a particle swarm algorithm.

[0114] Embodiment 2

[0115] This embodiment describes a satellite optimal collision avoidance control system integrating multiple factors, which is used for executing the satellite optimal collision avoidance control method integrating multiple factors of embodiment 1, and includes:

[0116] The first module is used for establishing the orbit differential equation of the collision target based on the Gauss perturbation equation, and describing the real-time motion state of the collision target.

[0117] The second module is used for establishing the continuous variable thrust direction angle function based on the Fourier series fitting.

[0118] The third module is used for establishing the optimal control model of the collision avoidance-return orbit integrating multiple factors.

[0119] The fourth module is used for solving the continuous thrust direction angle and the switching-on time, and realizing the optimal control of the mission satellite.

[0120] It can be understood that part of the present application not described in detail belongs to the known technology of those skilled in the art.

Claims

1. A multi-factor integrated satellite optimal collision avoidance control method, characterized in that, Comprise: The orbit differential equation of the mission star and the collision threat target based on the Gauss perturbation equation is established; the method for establishing the orbit differential equation of the mission star and the collision threat target based on the Gauss perturbation equation is: The state of the spacecraft in orbit is described by the orbital elements at each moment, and the differential equations of the orbital elements of the two colliding spacecrafts under continuous thrust are constructed by using Gauss perturbation equations, where the decomposition of the thrust in the tangential, normal and binormal directions of the velocity of the mission spacecraft is denoted as (f t ,f m ,f h ), and the differential equations of the orbit of the mission spacecraft are as follows: wherein the orbit elements of the mission satellite are is the derivative of the physical quantity with respect to time, a is the semi-major axis of the mission satellite, e is the eccentricity of the mission satellite, i is the inclination of the orbit of the mission satellite, Ω is the right ascension of the ascending node of the mission satellite, ω is the argument of the perigee of the mission satellite, u is the argument of latitude of the mission satellite, v is the orbital velocity of the mission satellite; p is the semi-latus rectum, θ is the true anomaly of the mission satellite, r is the geocentric distance of the mission satellite; f t is the tangential component of the thrust per unit mass of the mission satellite in the direction of the velocity vector of the mission satellite, f m is the normal component of the thrust per unit mass of the mission satellite in the direction away from the center of curvature in the orbital plane of the mission satellite, f h is the binormal component of the thrust per unit mass of the mission satellite in the direction of the momentum vector H of the mission satellite, e m is the unit vector in the tangential direction of the velocity of the mission satellite, e t is the unit vector in the normal direction of the velocity of the mission satellite, e h is the unit vector in the binormal direction of the velocity of the mission satellite, μ is the gravitational constant of the Earth; The orbit differential equation of the collision threat target is: Where, the orbit root number of the collision threat target is is the derivative of physical quantity with respect to time, a target is the semi-major axis of the collision target, e target is the eccentricity of the collision target, i target is the orbit inclination of the collision target, Ω target is the ascending node right ascension of the collision target, ω target is the argument of perigee of the collision target, u target is the latitude amplitude of the collision target star, v target is the orbit speed of the collision target; p target is the orbit half diameter, θ target is the true anomaly of the collision target, r target is the geocentric distance of the collision target; f ttarget is the tangential component of the perturbation force on the unit mass of the collision target along the forward direction of the velocity vector of the collision target, f mtarget is the normal component of the perturbation force on the unit mass of the collision target along the direction away from the curvature center in the plane of the orbit of the collision target, f htarget is the secondary normal component of the perturbation force on the unit mass of the collision target along the direction of the momentum moment vector H target of the collision target, e mtarget is the unit vector of the tangential velocity of the collision target, e ttarget is the unit vector of the normal velocity of the collision target, e htarget is the unit vector of the secondary normal velocity of the collision target, μ is the earth's gravitational constant; In the case that the thrust of the mission star at each time is known, the orbit differential equation of the mission star is integrated to obtain the orbit of the mission star under the control of the thrust, and the orbit differential equation of the collision threat target is integrated to obtain the orbit of the collision threat target without control; thus, the construction of the orbit differential equation of the collision target based on the Gauss perturbation equation is completed; The function of the direction angle of the continuous variable direction thrust based on the Fourier series fitting is established; the method for establishing the function of the direction angle of the continuous variable direction thrust based on the Fourier series fitting is: The expression formula of the continuous variable direction control thrust of the mission star is: Wherein, the component of the thrust F of the task star in the direction of (e m ,e t , e h ) is (F x ,F y ,F z );the thrust direction angle of the task star is (α,β), α is the angle between the projection of the task star thrust vector in the (e m ,e t ) plane and e m , the positive direction of the e h axis is positive, β is the angle between the task star thrust vector F and its projection in the (e m ,e t ) plane, the positive direction of the e h axis is positive; e m is the unit vector of the tangential velocity of the task star, e t is the unit vector of the normal velocity of the task star, e h is the unit vector of the subnormal velocity of the task star, (e m ,e t ) is the platform in which the tangential velocity of the task star and the normal velocity of the task star are located. In the expression formula of the continuous variable direction control thrust of the mission star, the change of the thrust direction angle (α, β) with time is described by the Fourier series fitting, and the function of the thrust direction angle based on the Fourier series fitting is: Wherein, the first item parameter, the second item parameter, the third item parameter, the fourth item parameter and the first item parameter of the Fourier series fitting of the thrust direction angle α are [a0, a1, a2, a3, a4], and the first item parameter, the second item parameter, the third item parameter, the fourth item parameter and the first item parameter of the Fourier series fitting of the thrust direction angle β are [b0, b1, b2, b3, b4]; The optimal control model of the collision avoidance-return orbit considering multiple factors is established in combination with the orbit differential equation and the function of the direction angle of the continuous variable direction thrust; the method for establishing the optimal control model of the collision avoidance-return orbit considering multiple factors in combination with the orbit differential equation and the function of the direction angle of the continuous variable direction thrust is: S031, the optimization variables of the collision avoidance-return orbit optimal control model are determined as: x=[a0, a1, a2, a3, a4, b0, b1, b2, b3, b4, t1, t2, t3] T Wherein, [a0, a1, a2, a3, a4, b0, b1, b2, b3, b4] are the first item parameters, the second item parameters, the third item parameters, the fourth item parameters and the first item parameters of the Fourier series fitting of the thrust direction angle α and the first item parameters, the second item parameters, the third item parameters, the fourth item parameters and the first item parameters of the Fourier series fitting of the thrust direction angle β; the moment when the collision threat target approaches the boundary of the anti-collision sensing range of the mission star is recorded as t=t0, the switch-on and switch-off moments of the two continuous thrust maneuvers are [t0, t1, t2, t3], wherein t0 is the first switch-on moment of the thruster, t1 is the first switch-off moment of the thruster, t2 is the second switch-on moment of the thruster, and t3 is the second switch-off moment of the thruster; the maneuver starts immediately when the collision threat target enters the boundary of the anti-collision sensing range of the mission star, so t0=0s is set. S032, the optimization constraints of the collision avoidance-return orbit optimal control model are determined as wherein Ax≤b is a linear constraint inequality, and the constraint parameters are: Wherein, A is the linear constraint matrix of the optimal control model of the mission star, x is the optimization variable of the optimal control model of the orbit of the mission star, and b is the linear constraint vector of the optimal control model of the orbit of the mission star; The upper and lower bound constraint inequality of the control quantity is lb < x < ub, and the constraint parameters are: where lb is the lower bound of the optimization variable of the mission star orbit optimal control model, ub is the upper bound of the optimization variable of the mission star orbit optimal control model, t is the time, and T is the maximum completion time of the single evasion control. max is the maximum completion time of the single evasion control. The nonlinear constraint function is c(x) ≤ 0, which is expressed as: wherein, (Δa final (x), Δe final (x), Δi final (x), ΔΩ final (x), Δω final (x), Δu final (x)) is the orbit root offset at the end of control, Δa final (x) is the semi-major axis offset of the mission star at the end of control, Δe final (x) is the eccentricity offset of the mission star at the end of control, Δi final (x) is the orbit inclination offset of the mission star at the end of control, ΔΩ final (x) is the right ascension of the ascending node offset of the mission star at the end of control, Δω final (x) is the argument of the perigee offset of the mission star at the end of control, Δu final (x) is the argument of the latitude offset of the mission star at the end of control, (Δa fmax , Δe fmax , Δi fmax , ΔΩ fmax , Δω fmax , Δu fmax ) is the maximum orbit root offset allowed for the mission star, Δa fmax is the maximum semi-major axis offset allowed for the mission star, Δe fmax is the maximum eccentricity offset allowed for the mission star, Δi fmax is the maximum orbit inclination offset allowed for the mission star, ΔΩ fmax is the maximum right ascension of the ascending node offset allowed for the mission star, Δω fmax is the maximum argument of the perigee offset allowed for the mission star, Δu fmax is the maximum argument of the latitude offset allowed for the mission star, l min (x) is the minimum safety distance of the mission star, l safe is the minimum safety distance of the mission star. S033, the objective function of the optimal control model of the collision avoidance-return orbit is: J = k1J1 + k2J2 + k3J3, Wherein, [J1, J2, J3] are the optimization objectives reflecting the mission factor, the optimization objectives reflecting the configuration factor and the optimization objectives reflecting the fuel factor respectively, [k1, k2, k3] are the first target weight, the second target weight and the third target weight, and the sum of the first target weight, the second target weight and the third target weight is 1; The optimization objective is set based on the weight allocation, the optimal solution of the optimal control model of the collision avoidance-return orbit is solved by an optimization algorithm, the continuous thrust direction angle and the switching time are obtained, and the mission star is controlled to avoid the collision threat target based on the continuous thrust direction angle and the switching time.

2. The method and system for optimal collision avoidance control of satellites considering multiple factors of claim 1, wherein In the objective function of the optimal control model of the collision avoidance-return orbit: where N cover (x) is the number of targets covered by the mission star, N target is the total number of targets covered; (Δu tmax (x),Δi tmax (x),ΔΩ tmax (x)) is the maximum value of the orbit root number offset of the whole course of the task satellite maneuver, Δu tmax (x) is the maximum value of the latitude amplitude angle offset of the whole course of the task satellite maneuver, Δi tmax (x) is the maximum value of the orbit inclination offset of the whole course of the task satellite maneuver, ΔΩ tmax (x) is the maximum value of the ascending node right ascension offset of the whole course of the task satellite maneuver, (Δu max ,Δi max ,ΔΩ max ) is the maximum orbit root number offset allowed by the task satellite, Δu max is the maximum latitude amplitude angle offset allowed by the task satellite, Δi max is the maximum orbit inclination offset allowed by the task satellite, ΔΩ max is the maximum ascending node right ascension offset allowed by the task satellite; t max The maximum fuel consumption allowed for a single avoidance of the task star corresponds to the on time, t1 is the first time the thruster is turned off, t2 is the second time the thruster is turned on, and t3 is the second time the thruster is turned off.

3. The method of claim 2, wherein, The optimization target is set based on the weight distribution, the optimal solution of the collision avoidance-return orbit optimal control model is solved through an optimization algorithm, and the continuous thrust direction angle and switching time are obtained. A method for controlling the mission star to avoid a collision threat target based on the continuous thrust direction angle and switching time is as follows: Optimization objective parameters [k1, k2, k3, J1, J2, J3] and constraint parameters [t max ,Δa fmax ,Δe fmax ,Δi fmax ,ΔΩ fmax ,Δω fmax ,Δu fmax ,l safe ] of the optimal control model of the mission-avoidance-returning orbit are set, wherein [J1, J2, J3] are an optimization objective embodying a mission factor, an optimization objective embodying a configuration factor and an optimization objective embodying a fuel factor, [k1, k2, k3] are a first objective weight, a second objective weight and a third objective weight, t max is a maximum completion time allowed for single avoidance control, Δa fmax is a maximum offset of the final semi-major axis allowed for the mission satellite, Δe fmax is a maximum offset of the final eccentricity allowed for the mission satellite, Δi fmax is a maximum offset of the final orbit inclination allowed for the mission satellite, ΔΩ fmax is a maximum offset of the final longitude of ascending node allowed for the mission satellite, Δω fmax is a maximum offset of the final argument of perigee allowed for the mission satellite, Δu fmax is a maximum offset of the final argument of latitude allowed for the mission satellite, and l safe is a minimum safety distance of collision avoidance of the mission satellite. On this basis, an initial value of the optimization variable x of the mission star orbit optimal control model is given, the collision avoidance-return orbit of the mission star under two continuous variable direction thrust maneuvers is solved through an optimization algorithm, the objective function of the collision avoidance-return orbit optimal control model is optimized under the condition of meeting the constraint condition, the optimal control strategy result, i.e., the thrust direction angle and switching time of the mission star, is obtained, and thus the optimal avoidance control of the mission star is realized.

4. The method of claim 3, wherein, The optimization algorithm is a nonlinear programming solver, a genetic algorithm, or a particle swarm algorithm.

5. A multi-factor integrated satellite optimal collision avoidance control system for performing the multi-factor integrated satellite optimal collision avoidance control method of any one of claims 1 to 4, characterized in that, The method comprises the following steps: A first module is configured to establish orbit differential equations of both collision targets based on a Gauss perturbation equation, and describe real-time motion states of both collision targets; A second module is configured to establish a continuous variable direction thrust direction angle function based on Fourier series fitting; A third module is configured to establish a collision avoidance-return orbit optimal control model considering multiple factors; A fourth module is configured to solve the continuous thrust direction angle and switching time, and realize optimal control of the mission star to avoid a collision.

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